Being small and rather fast, Kirin is the exception to the regular monsters in Monster Hunter. This also makes it quite difficult to develop hunting strategies that work flawlessly. As the weakness-diagram suggests, Kirin is more or less unaffected by elemental attacks, so the best you can do if you don’t either have a water or fire-element weapon, is to bring one that has high raw power. As for the battle itself try hit kirin when it’s resting after his series of jumps. You can also attack it when its executing his lightning attack, however the likelihood of getting hit is quite high.

The basic thing here is to take your time and play it safe. Kirins attacks might not be as fatal as others, but his quickness makes up for it and might get you into serious trouble.